A study of injection locking of non-coherent oscillators is described in Adler, "A Study of Locking Phenomenon in Oscillators," Proceedings of the IRE, June, 1946, pages 351-357. As described therein, the coherent bandwidth, .DELTA.F, of an injection locked oscillator is substantially equal to the ratio given by (1) the product of twice the frequency of the oscillator and the square root of the ratio of the injected coherent power to the output power of the oscillator to (2) the external Q of the oscillator.
The study of injection locking by Adler was further developed by others. For example, see Huntoon & Weiss, "Synchronization of Oscillators," Proceedings of the IRE, December, 1947, pages 1415-1423. The Huntoon reference provides a strong theoretical basis for injection locking regardless of circuit configuration.
One of the earlier articles relating to the injection locking of magnetron oscillators is given in David, "R. F. Phase Control and Pulsed Magnetrons," Proceedings of the IRE, June, 1952, pages 669-685. Although the theoretical concept of injection locking of magnetrons is known, the practical reduction to practice in the prior art of injection locked magnetrons has not been realized until relatively recently. First, appropriate low cost coherent sources of RF energy with sufficient power to drive magnetrons have not been available. Secondly, the existing magnetron circuits have an apparent limitation which limit the obtainable circuit bandwidth. The disadvantage resulting from this limitation is that the known magnetron circuits were insufficient for commercial exploitation.
Recent advances in solid state oscillators have all but eliminated the first limitation of the prior art noted above. Power levels for magnetrons are now aVailable in the 0.5 to 5.0 kilowatt level. With current devices, coherent gains of ten to thirteen dB are achievable over narrow bandwidths. The exploitation of these advances for magnetrons has, however, been limited by the ability of conventional magnetron circuits to present a sufficiently high impedance to the electron stream in the interaction region to sustain proper magnetron operation over a sufficiently wide bandwidth.
In a known prior art magnetron with a conventional circuit configuration, manipulation of the coupling between the conventional circuit and its external load will reduce its external Q. The reduction of the external Q will achieve a wider injection locking bandwidth. Because of the fundamental relationship between the external Q and the loaded Q, this will cause the fields on the magnetron circuit to become lower and lower until a phenomenon called "sink" is reached. At this point the magnetron ceases to work. The reason is that the total RF impedance of the circuit becomes too low to sustain oscillation.
The fundamental relationships which govern this sink phenomenon can be summarized as follows: EQU .DELTA.F=2F.sub.o (P.sub.i /P.sub.o).sup.1/2 /Q.sub.e EQU Z.sub.int =Q.sub.l (L/C).sup.1/2 EQU 1/Q.sub.l =1/Q.sub.o +1/Q.sub.e
wherein the locking bandwidth .DELTA.F is given by Adler's equation, Z.sub.int is the interaction impedance of the magnetron, Q.sub.o is the unloaded Q of the magnetron circuit and is a function of the frequency of the magnetron, Q.sub.l is the loaded Q of the circuit, Q.sub.e is the external Q of the circuit, and (L/C).sup.178 is the single cavity impedance of the magnetron and is a function of the configuration of the circuit.
From the above equations, it can be seen that the interaction impedance is the product of the loaded Q, Q.sub.l, and the single cavity impedance of the magnetron. Because of the fundamental relationship between the loaded Q, which is related to the ability to maintain oscillation, and the external Q, which is related to the ability to obtain large injection bandwidth, decreasing the external Q for a fixed circuit decreases the loaded Q. As a consequence thereof, the interaction impedance Z.sub.int, is also decreased.